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Let X1, X2, ., X be iid N(4, o?) with both u and o being unknown. (a) One estimator of o² is the sample variance S? = „ E:(X;-X)². Compute Mean Squared Error (MSE) of this estimator. (b) Consider an alternative estimator cS? with a constant c. Find the value of c to minimize MSE of this estimator. (c) Does any one of the two estimators above achieves the Cramér-Rao lower bound? Justify your answer.

Let X1, X2, ., X be iid N(4, o?) with both u and o being unknown. (a) One estimator of o² is the sample variance S? = „ E:(X;-X)². Compute Mean Squared Error (MSE) of this estimator. (b) Consider an alternative estimator cS? with a constant c. Find the value of c to minimize MSE of this estimator. (c) Does any one of the two estimators above achieves the Cramér-Rao lower bound? Justify your answer.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let X1, X2, ..., X, be iid N(u, o?) with both u and o being unknown. (a) One estimator of o² is the sample variance S? = „ DL(X;- X)². Compute Mean Squared Error (MSE) of this estimator. (b) Consider an alternative estimator cS with a constant c. Find the value of c to minimize MSE of this estimator. (c) Does any one of the two estimators above achieves the Cramér-Rao lower bound? Justify your answer.
Transcribed Image Text:Let X1, X2, ..., X, be iid N(u, o?) with both u and o being unknown. (a) One estimator of o² is the sample variance S? = „ DL(X;- X)². Compute Mean Squared Error (MSE) of this estimator. (b) Consider an alternative estimator cS with a constant c. Find the value of c to minimize MSE of this estimator. (c) Does any one of the two estimators above achieves the Cramér-Rao lower bound? Justify your answer.
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